Order In Ternary Alloys Research Articles

Ordered states in ternary B2-type intermetallic alloys including vacancies

Abstract The mean-field theory of order in ternary alloys is applied to the special case of vacancy-containing B2-type intermetallic alloys. In such alloys the vacancy content may be so large that the alloy should be treated as a ternary system, characterized by two long-range order parameters ξ and η in the Bragg–Williams approximation. At fixed overall concentrations of the three components and low temperatures the ternary system adopts essentially one of two possible states, having (ξ, η) pairs of unlike sign (state Ia) and like sign (state IIa) respectively. State Ia is characterized by defects on both sublattices (vacancies on the α sublattice and antisite a atoms on the β sublattice) whereas state IIa contains both defects on the β sublattice. These states can be transformed into each other by a reaction involving the interchange of vacancies and antisite a atoms with reaction energy B = εab – εaa (ε ij representing the pair interaction energy). From numerical computations of the free energy as a function of ξ,η and T, states Ia and IIa are found to be stable for B > 0 and B < 0 respectively, provided that the overall concentrations of atoms and vacancies are fixed. However, at thermodynamic equilibrium the vacancy content has to be adjusted at each temperature. For T → 0 this leads to two possible states, depending on the overall composition and the pair interactions. The first of these ground states is the classical vacancy-free B2 phase, whereas the second state (a special case of state IIa) contains structural vacancies in addition to b atoms on one sublattice to compensate for the excess a atoms on the other sublattice. The latter state is predicted to occur in off-stoichiometric alloys having components with quite different cohesive energies such as CoGa and NiAl, in qualitative agreement with experimental data on vacancies in some of these intermetallic compounds.

Ordered states in ternary B2-type intermetallic alloys including vacancies

Abstract The mean-field theory of order in ternary alloys is applied to the special case of vacancy-containing B2-type intermetallic alloys. In such alloys the vacancy content may be so large that the alloy should be treated as a ternary system, characterized by two long-range order parameters ξ and η in the Bragg–Williams approximation. At fixed overall concentrations of the three components and low temperatures the ternary system adopts essentially one of two possible states, having (ξ, η) pairs of unlike sign (state Ia) and like sign (state IIa) respectively. State Ia is characterized by defects on both sublattices (vacancies on the α sublattice and antisite a atoms on the β sublattice) whereas state IIa contains both defects on the β sublattice. These states can be transformed into each other by a reaction involving the interchange of vacancies and antisite a atoms with reaction energy B = εab – εaa (ε ij representing the pair interaction energy). From numerical computations of the free energy as a function of ξ,η and T, states Ia and IIa are found to be stable for B > 0 and B < 0 respectively, provided that the overall concentrations of atoms and vacancies are fixed. However, at thermodynamic equilibrium the vacancy content has to be adjusted at each temperature. For T → 0 this leads to two possible states, depending on the overall composition and the pair interactions. The first of these ground states is the classical vacancy-free B2 phase, whereas the second state (a special case of state IIa) contains structural vacancies in addition to b atoms on one sublattice to compensate for the excess a atoms on the other sublattice. The latter state is predicted to occur in off-stoichiometric alloys having components with quite different cohesive energies such as CoGa and NiAl, in qualitative agreement with experimental data on vacancies in some of these intermetallic compounds.

Recent Development in Quantitative Electron Diffraction for Crystallography of Materials

The present paper gives an extended review on applications of electron diffraction techniques to practical problems in materials science, such as (1) determination of structure factors and temperature factors by the critical voltage and intersecting Kikuchi line (IKL) methods, (2) measurement of local lattice parameters by convergent beam electron diffraction (CBED), (3) determination of partial degree of order in ternary alloys by IKL-ALCHEMI method, and (4) determination of structure factors by energy filtering CBED. The emphasis is placed on recent achievements of electron diffraction as a tool of quantitative crystallography of materials.

Ordering diagrams for ternary alloysA-B-(C) with an fcc lattice

The pattern of atomic ordering in ternary alloys A-B-(C) with an fcc lattice and L12 superstructure, in which the atoms of the component C occupy octahedral interstices, was investigated. The possible ordering diagrams of these systems were determined.

The Importance of Microstructural Instability in Determining the Mechanical Behaviour of Cubic Titanium Trialuminides

Cubic trialuminides deform by the movement of dislocations which are clearly dissociated as APB superdislocations at high temperatures, with debate about whether these are dissociated as APB or SISF superdislocations at low temperatures. These materials are characterized by the following mechanical behaviour: (i) strength variable with ternary element addition or titanium content; (ii) mild strength anomaly at high temperature, sometimes; (iii) serrations in stress-strain curve at intermediate temperatures; (iv) low tensile ductility (≈0) at room temperature, increasing at higher temperatures, with an intermediate temperature minimum. These properties are explained by the fine microstructure and its variation locally and with temperature: (a) a tetragonal component of order in ternary alloys in addition to the basic L12 order, varying with ternary element and content; (b) precipitation (sometimes on dislocations) during high temperature testing - accounting for the strength anomaly; (c) extra-ordinarily rapid solute collection at dislocations and APB's - accounting for strain aging and minimum ductility phenomena; (d) strain relaxation at crack tips restricted to single slip planes by the structural modification produced by shear - making a major contribution to brittleness. All these processes are particularly acute in the titanium trialuminides because of the structural instabilities involved, and the fast kinetics of atom rearrangement; thus low temperatures during testing or during cooling after prior heat treatment play a major role. Similar effects may be of importance in other intermetallics such as FeAl, TiAl.

Atomic ordering in ternary alloys with hcp structure of DO19 type

Atomic ordering is investigated in ternary substitution alloys with hexagonalclose-packed (hcp) structure of DO19(Ti3Al) type. The singularities are studied of the influence of the impurity of the third component C on the Kurnakov temperature and the degree of long-range order in the host atom arrangement. Phase diagrams are constructed for the ternary alloys with different values of the energy parameters and small concentrations of the component C. Changes in the phase diagram are analyzed for the binary alloy A-B upon addition of atoms C. Formulas are obtained to determine the energetic parameters of ternary alloys having a small concentration of one of the components. Computed as an illustration is a section of the phase diagram of the system Ti-Al-Fe and the iron atom distribution is studied over sites of the alloy crystalline lattice.

Anomalous scattering phenomena applied to the study of short-range order in ternary alloys

Anomalous scattering phenomena applied to the study of short-range order in ternary alloys

Ordering of ternary alloys in the self-consistent field approximation

In the self-consistent field approximation, without allowance for correlation, a static theory of the ordering of ternary alloys is constructed which makes it possible to take into account the long-range nature of the interatomic interaction forces in substitutional and interstitial alloys. The theory enables one to take into account the possible existence in the alloy of two subsets of points differing by the species of atoms that occupy them. The stability of the disordered state in such alloys is analyzed and an expression obtained for the temperature at which the disordered state loses stability.

A study by means of electron microscopy and electron diffraction of vacancy ordering in ternary alloys of the system AlCuNi

The structure and microstructure of ternary alloys in the system Al(Cu, Ni)1–x are studied by means of selected area electron diffraction and by means of lattice imaging. The long range ordered structures are derived from the CsCl structure, one of the sublattices being occupied by aluminium, the other one by metal atoms and vacancies. A number of composition related superstructures occurs; they are all based on the ordering of vacancies and metal atoms in (111) layers. A “transition” state can be identified in rapidly cooled specimens. Die Struktur und Mikrostruktur ternärer Legierungen im System Al(Cu, Ni)1–x werden mittels Elektronenbeugung ausgewählter Flächen und mittels Gitterabbildung untersucht. Die ferngeordneten Strukturen werden von der CsCl-Struktur abgeleitet, eines der Untergitter ist dabei von Aluminium, das andere von Metallatomen und Leerstellen besetzt. Es tritt eine Anzahl von Superstrukturen auf, die mit der Zusammensetzung verknüpft sind, sie basieren alle auf der Ordnung von Leerstellen und Metallatomen in (111)-Schichten. In schnell abgekühlten Proben kann ein “Übergangszustand” identifiziert werden.

Green's function treatment of ordered ternary alloy

AbstractA Green's function formulation of an ordered ternary alloy is given. The case of a two sub‐lattice system with nearest neighbour pair‐wise, static potentials is studied. A decoupling procedure similar to the molecular field approximation is carried out, and the resultant equations are analysed in detail. Conditions for the ternary order‐disorder transition to be of the second order variety are given, and order parameters are computed for several different potentials and concentrations, for which second order transition occurs. A few remarks concerning possible application of the Green's function method to the study of atomic diffusion and relaxation of spatial order in ternary alloys are also given.

Quasibinary ordering of ternary alloys

The problem of ordering in ternary alloys is considered for the case when a partially ordered phase is formed (quasibinary configuration of a ternary alloy). A. G. Khachaturyan's method is used to construct possible functions for the distribution of atoms over the points of the crystal lattice. A possible ternary superlattice is predicted for the case when the quasibinary configuration corresponds to the superlattice B2, L12, L10.

Atomic ordering in ternary alloys with hexagonal-close-packed structures. II

This paper constitutes a theoretical study of the influence of interstitial impurity atoms on the type of order-disorder transition in an alloy of the AB3-Cin type with an hcp structure. Allowance is made for a variety of types of interstices over the range 0 ≤η 1. The free energy is calculated by the Gorskii-Bragg-Williams method. In the presence of an impurity there may be a change in the magnitude of the jump taking place in the degree of long-range order at the transition point, and also a change in the type of order-disorder transition occurring.

The theory of atomic and magnetic ordering in ternary alloys with fcc lattice

We consider the theory of the mutual influence of atomic and spin ordering phenomena in ternary alloys of transition elements with fcc lattice. The case of quasibinary alloys B3A-B3D is considered in detail. Concentration dependences of the critical temperature of the order-disorder phase transition are considered for cases of atomic and magnetic ordering.

Sensitivity of ordering kinetics to the doping of Ni3Mn by iron, cobalt, and chromium

The changes in several physical and mechanical properties observed during the ordering of quenched ternary Ni3Mn-Ni3Me alloys (Me = Fe, Co, or Cr) were studied. Comparison of the results with results found previously by neutron diffraction shows that the latter method does not always give reliable information about the state of the ordering of ternary alloys, so it must be supplemented by a study of structure-sensitive physical and mechanical properties.

Theory of order in ternary alloys—II

A statistical theory of the order-disorder transformations for ternary alloys of arbitrary composition and crystal structure is given. Long-range and short-range order parameters are defined, and equations connecting these parameters are given. The general formula for configurational free energy is deduced and the method of calculation of the order-disorder transition temperature is shown. As examples the Heusler alloys Cu 2MnAl and Cu 2(MnAl) and the alloys AgMgSn are considered.

Theory of order in ternary alloys—I

The theory of order in ternary alloys as generalization of a theory of binary alloys is given. It is shown that for the description of the long-range order in ternary alloys a set of linear independent long-range parameters is needed. The number of these long-range parameters is fully determined. For the calculation of configurational energy, the method of finding the average number of pairs of atoms of mutual distance r is given. The long-range order is considered on basis of generalization of the Bragg-Williams theory. The general discussion of the thermodynamic equilibrium conditions of ternary alloys and the application of this theory to the Heusler alloy of composition Cu 2MnAl is also quoted.